Geodesic
K3 surfaces over number fields and $l$-adic representations
Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 575-595.

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The Tate conjecture on algebraic cycles is proved for any algebraic K3 surface over a number field. If the canonical representation of the Hodge group in the $\mathbf Q$-lattice of transcendental cohomology classes is absolutely irreducible, then the Mumford–Tate conjecture is true for such a K3 surface. Bibliography: 18 titles. 
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S. G. Tankeev. K3 surfaces over number fields and $l$-adic representations. Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 575-595. http://geodesic.mathdoc.fr/item/IM2_1989_33_3_a5/

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